In this paper, we give a Zariski triple of the arrangements for a smooth quartic and its four bitangents. A key criterion to distinguish the topology of such curves is given by a matrix related to the height pairing of rational points arising from three bitangent lines.
"A note on the topology of arrangements for a smooth plane quartic and its bitangent lines." Hiroshima Math. J. 49 (2) 289 - 302, July 2019. https://doi.org/10.32917/hmj/1564106549